The ratio in which $\widehat {\bf{i}} + 2\widehat {\bf{j}} + 3{\bf{\hat k}}$ divides the join of $ - 2\widehat {\bf{i}} + 3\widehat {\bf{j}} + 5\widehat {\bf{k}}$ and $7\widehat {\bf{i}} - {\bf{\hat k}}$ is

JEE MATHEMATICS MCQ: ADDITION OF VECTORS

1 Easy

1 of 1

Application +4 | -1

The ratio in which

\widehat \mathbf{i} + 2\widehat \mathbf{j} + 3\mathbf{\hat k}

divides the join of

- 2\widehat \mathbf{i} + 3\widehat \mathbf{j} + 5\widehat \mathbf{k}

and

7\widehat \mathbf{i} - \mathbf{\hat k}

View answer and explanation

Correct option: A

2:1

The correct answer is A. The ratio is found by using the section formula and equating the coefficients of the vectors.

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\mathbf{a}=\hat{\mathbf{i}}-\hat{\mathbf{j}}, \mathbf{b}=\hat{\mathbf{j}}-\hat{\mathbf{k}}

\mathbf{c}=\hat{\mathbf{k}}-\hat{\mathbf{i}}

\mathbf{d}

a

\mathbf{a} \cdot \mathbf{d}=0=(b \mathbf{c}

\mathbf{d}

{\mathbf{\vec a}}

2\;p

{\mathbf{\vec a}}

p + 1

\vec{a}, \vec{b}

\vec{c}

\vec{d}

\overrightarrow{\mathrm{a}}, \overrightarrow{\mathrm{b}}

\overrightarrow{\mathrm{c}}

|\overrightarrow{\mathrm{a}}+\overrightarrow{\mathrm{b}}+\overrightarrow{\mathrm{c}}+\overrightarrow{\mathrm{d}}|^2

\vec{a}, \vec{b}

\vec{c}

\vec{a}=8 \vec{b}

\vec{c}=-7 \vec{b}

\vec{a}

\vec{c}

2 \mathbf{i}+\mathbf{j}-\mathbf{k},-\mathbf{i}+2 \mathbf{j}+\lambda \mathbf{k}

-5 \mathbf{i}+2 \mathbf{j}-\mathbf{k}

\lambda

AD

ABC

E,\;BE

AC

F

AF:AC =